java - Rendering exponential and periodic Julia fractals -

i've read how render julia fractals here. i'm pretty thorough two-degree julia sets equations of form f(z)=z²+c don't know how render complex julia functions f(z) = e^z - 0.65 , other complex functions involve sine , cosine. how render these type of functions? also, color mapping should used in exponential functions?

for instance want achieve following image , others given on wikipedia page.

edit :

here tried:

complexnumber.java

package plane.complex;  /** * code>complexnumber</code> class implements complex numbers in java.  * includes basic operations can performed on complex numbers such as, * addition, subtraction, multiplication, conjugate, modulus , squaring.  * * @author      abdul fatir * @version      1.0 *  */ public class complexnumber { /** * real, re(z), part of <code>complexnumber</code>. */ private double real; /** * imaginary, im(z), part of <code>complexnumber</code>. */ private double imaginary; /** * constructs new <code>complexnumber</code> object both real , imaginary parts 0 (z = 0 + 0i). */ public complexnumber() {     real = 0.0;     imaginary = 0.0; }  /** * constructs new <code>complexnumber</code> object. * @param real real part, re(z), of complex number * @param imaginary imaginary part, im(z), of complex number */  public complexnumber(double real, double imaginary) {     this.real = real;     this.imaginary = imaginary; }  /** * adds <code>complexnumber</code> current complex number. * @param complex_number complex number added current complex number */  public void add(complexnumber complex_number) {     this.real = this.real + complex_number.real;     this.imaginary = this.imaginary + complex_number.imaginary; }  /** * complex conjugate of current complex number. * @return <code>complexnumber</code> object conjugate of current complex number */  public complexnumber conjugate() {     return new complexnumber(this.real,-this.imaginary); }  /** * modulus, magnitude or absolute value of current complex number. * @return magnitude or modulus of current complex number */  public double mod() {     return math.sqrt(math.pow(this.real,2) + math.pow(this.imaginary,2)); }  /** * square of current complex number. * @return <code>complexnumber</code> object square of current complex number */  public complexnumber square() {     double _real = this.real*this.real - this.imaginary*this.imaginary;     double _imaginary = 2*this.real*this.imaginary;     return new complexnumber(_real,_imaginary); }  /** * multiplies <code>complexnumber</code> current complex number. * @param complex_number complex number multiplied current complex number */  public void multiply(complexnumber complex_number) {     double _real = this.real*complex_number.real - this.imaginary*complex_number.imaginary;     double _imaginary = this.real*complex_number.imaginary + this.imaginary*complex_number.real;      this.real = _real;     this.imaginary = _imaginary; }  /** * prints complex number in x + yi format */ @override public string tostring() {     return this.real+" + "+this.imaginary+"i"; } /** * calculates exponential of <code>complexnumber</code> * @param complex_number input complex number * @return <code>complexnumber</code> e^(input complex_number) */ public static complexnumber exp(complexnumber complex_number) {     double = complex_number.real;     double b = complex_number.imaginary;     = math.exp(a)*math.cos(b);     b = math.exp(a)*math.sin(b);     return new complexnumber(a,b); } } 

here how tried render:

for(int x=0; x<width; x++)     {         for(int y=0; y<height; y++)         {             complexnumber oldz = new complexnumber();             complexnumber newz = new complexnumber(2.0*(x-width/2)/(width/2), 1.33*(y-height/2)/(height/2) );             int i;             for(i=0;i<max_iter; i++)             {                 oldz = newz;                 newz=complexnumber.exp(newz);                 newz.add(constant);                 if(newz.mod() > 2)                     break;             }             float brightness = < max_iter ? 1f : 0;             float hue = i%256 /255.0f;             color color = color.gethsbcolor(hue, saturation, brightness);             img.setrgb(x,y, color);         }     } 

in exp function, used value a again after changing it, requiring in unchanged version. replace with

public static complexnumber exp(complexnumber complex_number) {     double = complex_number.real;     double b = complex_number.imaginary;     double r = math.exp(a);     = r*math.cos(b);     b = r*math.sin(b);     return new complexnumber(a,b); }